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Periodic Monopoles and Difference Modules by Takuro Mochizuki at Abbey's Bookshop,
Periodic Monopoles and Difference Modules
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Takuro Mochizuki

Periodic Monopoles and Difference Modules

Takuro Mochizuki

$147.95   $118.08

Paperback

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English
Springer Nature Switzerland AG
24 February 2022
Differential & Riemannian geometry; Algebraic geometry; Mathematical physics
Series: Lecture Notes in Mathematics
This book studies a class of monopoles defined by certain mild conditions, called periodic monopoles of generalized Cherkis–Kapustin (GCK) type. It presents a classification of the latter in terms of difference modules with parabolic structure, revealing a kind of Kobayashi–Hitchin correspondence between differential geometric objects and algebraic objects. It also clarifies the asymptotic behaviour of these monopoles around infinity. The theory of periodic monopoles of GCK type has applications to Yang–Mills theory in differential geometry and to the study of difference modules in dynamical algebraic geometry. A complete account of the theory is given, including major generalizations of results due to Charbonneau, Cherkis, Hurtubise, Kapustin, and others, and a new and original generalization of the nonabelian Hodge correspondence first studied by Corlette, Donaldson, Hitchin and Simpson. This work will be of interest to graduatestudents and researchers in differential and algebraic geometry, as well as in mathematical physics.
By:  
Imprint:   Springer Nature Switzerland AG
Country of Publication:   Switzerland
Edition:   1st ed. 2022
Volume:   2300
Dimensions:   Height: 235mm,  Width: 155mm, 
Weight:   528g
ISBN:   9783030944995
ISBN 10:   3030944999
Series:   Lecture Notes in Mathematics
Pages:   324
Publication Date:  
Audience:   Professional and scholarly ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active

Takuro Mochizuki has been awarded the 2022 Breakthrough Prize in Mathematics for advancing the understanding of holonomic D-modules through his research on harmonic bundles and twister D-modules, which he has studied at the ""interface of algebraic geometry and differential geometry"".

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